Biomedical Engineering Reference
In-Depth Information
minimum concentration is around 0.2
1 wt%, depending on M
w
, but accessing very high
concentrations is normally limited by solubility. Attempts to apply the Eldridge
-
Ferry
melting law to these samples are also limited by both solubility and the large gap between
formation and remelting. Evidence from Matsuhashi (
1990
) suggests that, at higher
concentrations, the melting point becomes more concentration-independent. That said,
some published data exists, including the extensive work by Watase and Nishinari and
co-workers. This is discussed in more detail below.
-
7.3.3.2
Effect of molecular mass
One piece of work (Watase and Nishinari,
1983
) was one of the
first to investigate the M
w
dependence of mechanical properties. Initially they prepared a series of agarose samples,
at a
fixed concentration but with a range of M
w
from 3.4 to 48.5 × 10
4
g mol
−
1
, and
measured the time-dependent Young
s modulus E(t) by stress relaxation. As expected, at
lowM
w
there was a tendency for some stress to relax, but this was not seen for the highest
M
w
sample. They also measured the storage Young
'
s modulus E
0
for the same samples by
the longitudinal vibration method, so avoiding slippage. Values were found for all except
the highest M
w
samples, where solubility again appeared to be a problem. They then used
Poisson
'
s ratio (0.5) to evaluate the corresponding shear moduli, and obtained values of
G
0
as a function of both concentration and M
w
. The data, when plotted as log G
0
versus
log c, shows the expected behaviour, that is, not a single power law but a curve with an
increasing slope as c approaches the minimum concentration c
0
. At the highest concen-
trations, the slope appears to be slightly less than 2. In a separate study, Tokita and
Hikichi (
1987
) analysed the concentration range closer to c
0
with a power-law model and
found the expected higher exponent, in their case around 4.
An attempt was made by Watase and co-workers (Watase et al.,
1989
) to analyse the
overall data using a two-dimensional branching theory model (i.e. both c and M
w
'
tted
simultaneously). The critical concentrations found in this
fit were a decreasing
function of M
w
, as might be predicted, but were found to lie approximately in the range
0.02
'
global
'
2 wt%. For the higher M
w
samples, this was substantially below that found by
analysing each M
w
set separately (0.2
-
-
2%). In the latter case the log M
w
dependence of
log c
0
was close to the ideal value of
1. Perhaps unsurprisingly in view of the modulus
and temperature behaviours reported above, analyses of the relaxation spectra of agarose
gels of the different molecular masses reported by Watase and Nishinari (
1983
) showed a
clear dependence on M
w
, the highest M
w
samples extending into the longer time region.
Work by Normand and co-workers (Normand et al.,
2000
) has re-examined both the
small- and large-deformation behaviour of agarose gels for three different M
w
samples
and a range of concentrations. Their small-deformation rate data has been used to
superimpose the gelation curves
−
-
but they report an observed modulus concentration exponent of 2.1, although the usual
curvature is seen. In fact a more useful comparison comes from their initial large-
deformation measurements, and they report a slope of log E (measured under both
tension and compression, although the exponents for the same samples differ slightly)
versus log c of 2.6 at low concentrations and 1.5 at the highest concentrations. More
detailed discussion of these results is given in
Section 7.3.3.5
.
-
a method upheld by these workers for other systems
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